# Network depth: identifying median and contours in complex networks

## TL;DR

This paper introduces a new method to identify the central node in complex networks by generalizing the median concept using a novel statistical data depth, applicable to networks embedded in geometric spaces, with practical relevance in social and biological contexts.

## Contribution

It proposes a new median concept for complex networks based on statistical data depth, enhancing the identification of central nodes in various network types.

## Key findings

- New median concept effectively identifies central nodes
- Applicable to networks embedded in geometric spaces
- Reveals socially and biologically relevant median nodes

## Abstract

Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be considered as the `centre' of a complex network. In fact, this problem corresponds to finding the median of a complex network. The median is a non-parametric and robust estimator of the location parameter of a probability distribution. In this work, we present the most natural generalisation of the concept of median to the realm of complex networks, discussing its advantages for defining the centre of the system and percentiles around that centre. To this aim, we introduce a new statistical data depth and we apply it to networks embedded in a geometric space induced by different metrics. The application of our framework to empirical networks allows us to identify median nodes which are socially or biologically relevant.